In prior art foil stretching machines, non-pivotable clips or the clamping parts of such clips are used in order to grasp a film to be stretched in the inlet area of the machine, to convey the film in the longitudinal film direction which is the transport direction of the film for stretching the film crosswise within a treatment area of an oven. In order additionally to shrink the film in the longitudinal direction after stretching, it is known to shorten the pitch of the chains for lengthwise shrinking the previously stretched film. However the alteration of the chain pitch is structurally expensive. In addition, the chain has to transfer high forces as a result of which highly stressed connections have to be provided between the chain links.